Questions: -3x - 3 < -x - 5

Solution Steps

To solve the inequality $-3x - 3 < -x - 5$, we need to isolate $x$ on one side of the inequality. We will first add $3x$ to both sides, then add $5$ to both sides, and finally divide by the coefficient of $x$ to solve for $x$. Once we have the solution, we will express it in interval notation.

First, we start by simplifying the given inequality: $$-3x - 3 < -x - 5$$

Add $3x$ to both sides of the inequality to move all terms involving $x$ to one side: $$-3x + 3x - 3 < -x + 3x - 5$$ This simplifies to: $$-3 < 2x - 5$$

Next, add 5 to both sides to isolate the term involving $x$: $$-3 + 5 < 2x - 5 + 5$$ This simplifies to: $$2 < 2x$$

Divide both sides by 2 to solve for $x$: $$\frac{2}{2} < \frac{2x}{2}$$ This simplifies to: $$1 < x$$ or equivalently: $$x > 1$$

Final Answer